Trimodal extension based on the flexible generalized skew-normal distribution

We propose a novel class of generalized skew-normal densities that improvesthe flexibility of empirical distributions and can systematically capture skewness,heavy tails, and multimodality. We extend the so-called flexible generalized skewnormal(FGSN) density developed by Y. Ma and M.G. Genton in 2004. The mainnovelty is the existence of a fifth-order degree term in the polynomial that appearsin the cumulative distribution function of such a density. In this case, we provethat our density has at most three modes under certain conditions for the parameters.Leveraging this new approach eases the modeling of data consisting of threesubpopulations. For validation, we present examples of both univariate and multivariatecases using demographic data from the Human Mortality Data Base (HMD).